In thin-film mixtures of alcohol and water, differences in evaporation rates and surface tensions between the two liquids can cause what is known as Marangoni convection within the fluid. This can lead to the formation of interesting instabilities on the surface of the film, such as the commonly observed “wine tears” phenomenon. Similar instabilities are observed when an inclined plate is immersed in a water alcohol reservoir. In addition to the tears, small ridges can be observed where the thin-film along the side of the plate rejoins the larger reservoir. These ridges slowly drift to the side and merge with other ridges, coarsening into larger ones. Using lubrication theory, Hosoi and Bush developed a one-dimensional model of the ridge instability which takes into account gravity, capillarity and Marangoni stresses at the surface of the film and results in a fourth-order non-linear partial differential equation describing the height of the ridges as a function of time and position along the plate. Two different but complementary numerical models were implemented to solve their equation. Both models are able to show development of ridges from random initial conditions as well as lateral ridge movement and coarsening. In addition to the numerical approaches some analysis was done on the equation to gain further insight into the nature of the ridge coarsening.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1153 |
| Date | 01 May 2003 |
| Creators | Lamb, Peter |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
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